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%I #17 Sep 06 2020 03:45:46
%S 1,1,1,1,1,4,1,1,9,36,1,4,4,4,9,9,1,4,1,4,4,4,1,4,100,100,900,900,36,
%T 144,9,9,9,36,25,100,100,100,9,36,4,4,4,4,900,3600,225,900,1764,1764,
%U 1764,1764,196,784,4,4,4,16,4,16,16,16,441,441,49,196,49,196,36,36,1,4
%N The largest square which divides n-th central binomial coefficient.
%H Amiram Eldar, <a href="/A056057/b056057.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A008833(A001405(n)).
%F a(A046098(n)) = 1.
%t Table[First@ Select[Reverse@ Divisors@ Binomial[n, Floor[n/2]], IntegerQ@ Sqrt@ # &], {n, 72}] (* _Michael De Vlieger_, Feb 18 2017 *)
%t a[n_] := Times @@ (First[#]^(2*Floor[Last[#]/2]) & /@ FactorInteger[Binomial[n, Floor[n/2]]]); Array[a, 100] (* _Amiram Eldar_, Sep 06 2020 *)
%Y Cf. A001405, A000188, A008833, A007913, A055229, A055231, A046098, A034974.
%Y Cf. A056056, A056058, A056059, A056060, A056061.
%K nonn
%O 1,6
%A _Labos Elemer_, Jul 26 2000
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